Well, it's a different parameter space, that's all.

We tend to operate in the usual 6-dimensional parameter space for everything we do (3 position vectors, 3 speed vectors), but there are equivalent parameter spaces that do the job just as well. In some cases, the alternate spaces are more useful - polar coordinates are the most common example.

The paper quoted in the article found a parameter space where very interesting transformations and symmetries take place.

This is exacly right, and it's a shame that article pushes the "woo, magic" perspective, instead of using the opportunity to highlight the little-known fact (among the lay public and students) of theoretical phyisics: it's a about model-building, "dimensions" aren't real except in the sense that a certain mathematical model (with N dimensions) is (a) consistent with experiment, and (b) has a lot of symmetry and simplicity relative to its explanatory/predictive power.

TBH, when you stumble upon a really useful parameter space, it does seem like magic.

Also, these days I'm reading Max Tegmark's "Our Mathematical Universe" and, being immersed in that argumentation, the whole "real vs unreal" dichotomy seems a bit transparent. Anyway, having formerly played a bit with computational physics, I'm primarily after what's useful.

General semantics helped me be aware of how easy it is to confuse the map for the territory, as well as adopt models based on their usefulness. As a great philosopher once said, reality is what you can get away with.

I was a little sad to learn that because KSP's orbital model uses conic sections, it's not physically accurate enough to model things like Lagrange points.

Then I remembered that it's still accurate enough to be awesome and stopped worrying about it. :)

Actually Newtonian Conic Sections is how we (humans) calculated orbital, and interplanetary trajectories up until the 1980's.

There weren't powerful enough computers to model full Eisenstein N-Bodies Systems until actually very recently (also its complete over kill for inner-solar system travel). Relativity is really complex math, and even modern computer clusters struggle to model very complex systems.

Yes we sent astronauts to the moon using KSP math.

> Yes we sent astronauts to the moon using KSP math.

I'm almost positive that we did not.

While patched conics would have been used very early on for rough mission analysis and design, we had a very good understanding of perturbation theory at the time. Wikipedia tells me that the restricted 3-body problem was also essentially solved in 1917. I've seen very detailed plots of the free return trajectories that the Apollo missions followed, too.

Using patched conics for the earth moon system would have resulted in an error on the scale of lunar escape velocity upon entering the sphere of influence of the Moon.

>I've seen very detailed plots of the free return trajectories that the Apollo missions followed, too.

Free return trajectories can be calculated with patched conics. 3 Body problem was solved, but actually doing all the math involved dynamically was far to complex for mission computers.

You forget that at the time NASA was using IBM System/360's which were struggling to maintain 5 megaFLOPs

I get that the idea that we "went to the moon with a slide rule" and similar ideas are appealing, but I'm not convinced that your statements are resting on a basis of fact.

For one thing, I'm not convinced that your mental models of what a "mission computer" is and what a "mission computer" would be doing, or when, make sense from an engineering perspective. I'm also not convinced that you know what an orbital perturbation is, nor how they would be used to plan and fly a mission.

To take an example from aviation, we didn't have practical simulations of general viscous fluid flow in the 1960s, but it would be meaningless to say that we "used Bernoulli's principle" to fly across the Pacific.

The Apollo vehicles had an on-board IMU. A trajectory could thus be pre-planned and flown to using feedback control. That trajectory would certainly have been calculated ahead of time. Thus, while there would be no need to have "[done] the math involved dynamically," that by no means implies that patched conics were used while in flight, nor does it imply that they were in any meaningful way used for the final design of the missions' flight paths.

Further, on any deviation from the planned flight path, numerical integration methods would yield results that would be good enough for later correction, again, by using feedback control.

If you still need to believe that "KSP math" is how we got to the Moon, go ahead. You've certainly done nothing to convince anyone else, though.

Thankfully, we only used KSP math, and not KSP engineering.

Aren't Lagrange points present in Newton's model? Why would they be missing from the game?

They're missing from KSP not merely because it uses Newtonian physics, but because it only uses two-body gravitational physics at any given time. The planets and moons are on rails and you are in only one gravity well at a time. Lagrange points exist in the intersections between two gravity wells.

Well if you're still interested in following the ongoing work to change that check out Principia :)

http://forum.kerbalspaceprogram.com/threads/68502-WIP-Princi... https://github.com/mockingbirdnest/Principia

I thought for a second you were facetiously referring to Philosophiae Naturalis Principia Mathematica... "hey, check out this cool new work on orbital mechanics" :P

As a matter of fact, I think that its simplicity is what makes KSP so fun to play. If it was real n-body orbital mechanics with real drag the game would quickly become much too complicated and tedious for casual play (and too slow).

Yup. One of the Fun things that are less known that comes from n-body orbital mechanics is the instability of orbits. You can't just leave your satellite out there and fast-forward two years because you have an Eve mission going - your satellite needs to make correction burns as other bodies perturb its orbit.

http://en.wikipedia.org/wiki/Orbital_station-keeping

But anyway, I still hope that Principia mod (the n-body simulation addon mentioned elsewhere in this thread) will get released. This will really bring KSP into Dwarf Fortress level of enjoyment. Also, you'd get to make some really weird-ass stuff:

http://images.scholarpedia.org/w/images/f/f6/NbodyChoreoGamm...

http://tuvalu.santafe.edu/~moore/crisscross123.loop.gif

For broader accessibility: a system like Civ's, where the system can play itself / do computations for you, but lets you dial up the amount of player-control.

You have MechJeb mod for that.

With barely 200 hours of flight under my belt, I think I haven't played the game enough, because I haven't reached that intuition yet to see this article's insight as obvious. What this means, of course, is that I need to go back playing more KSP :).

Seriously, it's amazing how this game can let you understand space travel and make you want to know the math behind it.

Here's the shortest, sweetest "a-ha" I've yet learned in KSP.

So you're piloting ship A and you want to rendezvous with ship B in a stable orbit. Let's assume that A and B are on identical, basically circular orbits, and A is behind B, so your distances from each other aren't really changing much.

The maneuver you're looking for is.... Point retrograde (i.e. "away from the direction that will take you to where B is now") and burn. In the short run, you increase your distance from B (of course), but you also dropped your orbital altitude and therefore the area of the arc swept between your ship and your center of orbit over time... and by Kepler's second law, you are now orbiting faster (more full revolutions per unit of time). So you'll swing under B and eventually come up "in front" of it; time your burns right, and you come up epsilon distance in front of B; rendezvous successful.

It's totally counter-intuitive to accelerate away from something to approach it, except you're basically on a sphere. :-p

Agreed, and I had played over 200 hours of KSP before I really got a handle on rendezvous, and had many failed attempts before intuitively getting it, and it becoming easy.

After that point no maneuver was daunting in KSP, just something that was a matter of time and making sure I quick save occasionally.

How can you subtract gravity from an orbit and end up with a circle?

If you have no gravity the particle will simply move in a straight line, and that's not a motion I would call an orbit.

You're absolutely right, of course. I was talking about the "time-gravity" component they subtract in the article to circularize the orbit, not all of gravity.

During an orbit, gravity is of course stronger when you're near the planet, and weaker when you're away from the planet. So they equalize the gravity by subtracting the relative time/gravity differential and calling it a separate dimension.

This leaves a constant gravity force and velocity, making certain calculations and transformations more natural in this model.